Example.—Required the area of a segment less than a semicircle, the radius being 20 inches, the chord 22·42 inches, the length of the arc 24·43 inches, and the perpendicular 16·56 inches.
24·43 × 20 2 = 244·3 square inches. Area of the sector.
22·42 × 16·56 2 = 185·6376 square inches. Area of the triangle.
244·3 - 185·6376 = 58·6624 square inches. Area required.
To find the area of a semicircle.
1. Multiply ¼ of the circumference by the radius, and the product will be the area.
2. Or, multiply the square of the diameter by ·7854, and half the product will be the area.
Example.—Rule 2.—Required the area of a semicircle, the diameter being 50 inches.
50 × 50 × ·7854 2 = 981·75 square inches. Area required.
To find the area of an ellipsis, or oval.
Multiply the longest diameter, or axis, by the shortest, then multiply the product by ·7854 for the area.
Example.—Required the area of the ellipse, whose diameters are 25 inches, and 18 inches.